Spray and Wait: An Efficient Routing Scheme for Intermittently Connected Mobile Networks

1. Spray and Wait: An Efficient Routing Scheme forIntermittently Connected Mobile Networks Authors: Thrasyvoulos Spyropoulos, Konstantinos Psounis, and Cauligi S. Raghavendra (All from the University of Southern California) SIGCOMM WTDN Workshop-2005, Philadelphia

2. Abstract Intermittently Connected Mobile Networks (ICMN) These fall into the general category of Delay Tolerant Networks Some networks that follow this paradigm are: Wildlife tracking sensor networks Military networks Inter-planetary networks In such networks conventional routing schemes such as DSR & AODV would fail

3. An example of Intermittently Connected Mobile Networks (ICMN)

4. A possible solution Store-carry-and-forward: Node mobility needs to be exploited in order to overcome the lack of end-to-end connectivity and deliver a message to its destination

5. Existing Proposals Flooding: everyone gets a copy (Epidemic Routing - Vahdat et al. ‘00): Note: optimal delay only when traffic is very low! Reducing the overhead of flooding Randomized Flooding (Y. Tseng et al. ‘02) : handover a copy with probability p < 1 Utility-based Flooding (A. Lindgren et al. ‘03) : handover a copy to a node with a utility at least Uth higher than current Can use p and Uth to tradeoff transmissions for delay, BUT: A number of approaches can be taken to reduce the transmission of epidemic routing and improve its performance. One is to hand over a message with some probability smaller than 1. A more sophisticated one is to maintain a utility function, and handover a message only to node with a utility at least Uth higher than the current value. One can therefore use the forwarding probability or the utility threshold to tradeoff transmissions for delay. However, they’re still flooding-based in nature. Furthermore, they are faced by the following dilemma. If a low probability or high threshold is used, many transmissions can be saved, but delay is increased significantly as we shall see. If a high probability or low threshold is used these protocols degenerate to flooding. In other words, these protocols are not flexible enough to significantly improve the performance of epidemic routing in many scenarios. A number of approaches can be taken to reduce the transmission of epidemic routing and improve its performance. One is to hand over a message with some probability smaller than 1. A more sophisticated one is to maintain a utility function, and handover a message only to node with a utility at least Uth higher than the current value. One can therefore use the forwarding probability or the utility threshold to tradeoff transmissions for delay. However, they’re still flooding-based in nature. Furthermore, they are faced by the following dilemma. If a low probability or high threshold is used, many transmissions can be saved, but delay is increased significantly as we shall see. If a high probability or low threshold is used these protocols degenerate to flooding. In other words, these protocols are not flexible enough to significantly improve the performance of epidemic routing in many scenarios.

6. Existing Proposals (cont’d) Single-copy solutions (Spyropoulos et al. ’04) Only one copy per message at any time Randomized, utility-based, hybrid, etc. Significantly reduced transmissions, BUT high delay Redundant copies reduce delay Too much redundancy is wasteful and often disastrous! Summarizing: No existing protocol has both low transmissions and low delay! Proposed Approach: Spray and Wait Finally, on can employ single-copy solutions that only generate and route one copy of the message. Such schemes can reduce transmissions significantly, but usually incur an important delay penalty. Summarizing, no existing protocol has both low transmissions and low delay. Finally, on can employ single-copy solutions that only generate and route one copy of the message. Such schemes can reduce transmissions significantly, but usually incur an important delay penalty. Summarizing, no existing protocol has both low transmissions and low delay.

7. Definition Definition 3.1 : Spray and Wait routing consists of the following two phases: Spray phase: For every message originating at a source node, L message copies are initially spread to L distinct “relays” Wait phase: If the destination is not found in the spraying phase, each of the L nodes carrying a message copy performs direct transmission (i.e. will forward the message only to its destination)

8. Spraying Matters Source Spraying – Slowest source distributes all L copies one by one; Binary Spraying – Optimal source starts with L copies whenever a node with n > 1 copies finds a new node, it hands over half of the copies that it carries The source of a message initially starts with L copies; any node A that has n > 1 message copies, and encounters another node B with no copies, hands over to B, n/2 and keeps n/2 for itself; when it is left with only one copy, it switches to direct transmission An important issue here is how these L copies are distributed to L relays, during the spraying phase One method is to have the source node distribute all copies, one-by-one, to L different nodes it encounters. A better way is following. Initially the source starts with L copies. Then, whenever a node with more than 1 copies finds a new node, it hands over to it half of its copies. This method is optimal Intuition: READ IT!An important issue here is how these L copies are distributed to L relays, during the spraying phase One method is to have the source node distribute all copies, one-by-one, to L different nodes it encounters. A better way is following. Initially the source starts with L copies. Then, whenever a node with more than 1 copies finds a new node, it hands over to it half of its copies. This method is optimal Intuition: READ IT!

9. Binary Spray & Wait proof of optimality: intuition: when movement is I.I.D., any two nodes will find on average an equal number of potential relays in the same amount of time Theorem 3.1: When all nodes move in an IID manner, Binary Spray and Wait routing is optimal, that is, has the minimum expected delay among all spray and wait routing algorithms Proof: Let us call a node active when it has more than one copies of a message. Let us further define a spraying algorithm in terms of a function f : N ? N as follows When an active node with n copies encounters another node, it hands over to it f(n) copies, and keeps the remaining n- f(n) since only active nodes may hand over additional copies, the higher the number of active nodes when i copies are spread, the smaller the residual expected delay Since the total number of tree nodes is fixed (21+log L - 1) for any spraying function f, it is easy to see that the tree structure that has the maximum number of nodes at every level, also has the maximum number of active nodes at every step.

10. Delay of Spray and Wait An Upper Bound Assume nodes moving independently with random walks/random waypoint and no contention Lemma 4.1: Let M nodes with transmission range K perform independent random walks on a torus. The expected delay of Direct Transmission is exponentially distributed with average (Aldous et al. ’01; Spyropoulos et al. ’04) The expected delay of the Optimal algorithm is:

11. Delay of Spray and Wait An Upper Bound Exact delay can be calculated using a system of recursive equations, but is not in closed form – Derive a bound: In order to do so, we need to calculate the delay of Spray and Wait as a function of this number of copies. We will assume that all nodes perform independent random walks and that there is no contention. Although the exact delay can be calculated using a system of recursive equations it is not in closed form. Therefore we will derive a tight upper bound, instead. Specifically, the delay of spray and wait is at most the expected time to spray all L copies ES, plus the duration of the wait phase EW, times the probability that the destination was not found during the spraying phase. Now let us look into the delay of the wait and spray phases separately In order to do so, we need to calculate the delay of Spray and Wait as a function of this number of copies. We will assume that all nodes perform independent random walks and that there is no contention. Although the exact delay can be calculated using a system of recursive equations it is not in closed form. Therefore we will derive a tight upper bound, instead. Specifically, the delay of spray and wait is at most the expected time to spray all L copies ES, plus the duration of the wait phase EW, times the probability that the destination was not found during the spraying phase. Now let us look into the delay of the wait and spray phases separately

12. Performance of Spray and WaitDelay of Wait Phase In the wait phase there are L relays that each carries a copy, shown here in red color. Now, the time until a given relay encounters the destination is exponentially distributed with average EDdt (which is the expected delay of direct transmission that is known). Consequently, the expected time until any of the L relays encounters the destination, that is the duration of the wait phase is equal to EDdt over LIn the wait phase there are L relays that each carries a copy, shown here in red color. Now, the time until a given relay encounters the destination is exponentially distributed with average EDdt (which is the expected delay of direct transmission that is known). Consequently, the expected time until any of the L relays encounters the destination, that is the duration of the wait phase is equal to EDdt over L

13. Performance of Spray and WaitDelay of Spray Phase Let us now look into the spraying phase. We assume that the source distributes all L copies. Again, the time until the source encounters the first relay is EDdt over M-1 since there are M-1 other nodes. Then, the time until the second relay is encounter by the source is EDdt over M-2 since now M-2 nodes have no message copy. Summing up this way the time until L-1 different relays are encountered we get the expected delay of the Spraying phase. Putting all together we get the upper bound equation, which is an upper bound because a) we assume that the source distributes all copies, and b) because we assume that the whole spraying phase is needed, even if the destination is encountered before L copies are distributed.Let us now look into the spraying phase. We assume that the source distributes all L copies. Again, the time until the source encounters the first relay is EDdt over M-1 since there are M-1 other nodes. Then, the time until the second relay is encounter by the source is EDdt over M-2 since now M-2 nodes have no message copy. Summing up this way the time until L-1 different relays are encountered we get the expected delay of the Spraying phase. Putting all together we get the upper bound equation, which is an upper bound because a) we assume that the source distributes all copies, and b) because we assume that the whole spraying phase is needed, even if the destination is encountered before L copies are distributed.

14. Choosing L to Achieve a RequiredExpected Delay Assume that there is a specific delivery delay constraint to be met. This delay constraint is expressed as a factor a times of the optimal delay EDopt (a > 1) Lemma 4.3: The minimum number of copies Lmin needed for Spray and Wait to achieve an expected delay at most a *EDopt, is independent of the size of the network N and transmission range K, and only depends on a and the number of nodes M By letting EDsw = a*EDopt

15. What If Network Parameters Are Unknown?Online Parameter Estimation Now the previous calculations assume that each node knows the total number of nodes M in the network. However, in practice this might be not known. In order to be able to optimize Spray and Wait even in situations like that, we would like to somehow produce and maintain online a relatively accurate estimate of the total number of nodes. This is a difficult problem in general. Our idea is to take advantage of meeting time statistics for random walks. We know that the time until any other node is encountered by a given node is EDdt over M-1. We call this T1 Similarly the expected time until a node encounters any two DISTINCT nodes T2 is (read). Solving these two for M we get an estimate that depends on T1 and T2 We can thus collect samples and maintain a running average of T1 and T2 and thus produce an estimate of M. As it can be seen by the plot this estimate converges to its actual value after a number of samples Although we have described our method assuming the random walk model, this method can be used for any mobility model for which meeting times are exponentially distributed. We have also applied to the random waypoint case and it performs equally wellNow the previous calculations assume that each node knows the total number of nodes M in the network. However, in practice this might be not known. In order to be able to optimize Spray and Wait even in situations like that, we would like to somehow produce and maintain online a relatively accurate estimate of the total number of nodes. This is a difficult problem in general. Our idea is to take advantage of meeting time statistics for random walks. We know that the time until any other node is encountered by a given node is EDdt over M-1. We call this T1 Similarly the expected time until a node encounters any two DISTINCT nodes T2 is (read). Solving these two for M we get an estimate that depends on T1 and T2 We can thus collect samples and maintain a running average of T1 and T2 and thus produce an estimate of M. As it can be seen by the plot this estimate converges to its actual value after a number of samples Although we have described our method assuming the random walk model, this method can be used for any mobility model for which meeting times are exponentially distributed. We have also applied to the random waypoint case and it performs equally well

16. Scalability of Spray and Wait Spray and Wait: M? ? ? Spray and Wait actually decreases the transmissions per node as the number of nodes M increases In contrast: in flooding, transmissions grow linearly with M Also, the performance of Spray & Wait improves faster than optimal scheme !!! This can be proved using Lemma 4.4

17. Scalability of Spray and Wait Lemma 4.4: Let Lmin(M) denote the minimum number of copies needed by Spray and Wait to achieve an expected delay that is at most a *EDopt, for some a. Then Lmin(M)/M is a decreasing function of M.

18. Scenario A : Effect of Traffic Load Assumptions: 100 nodes move according to the random waypoint model in a 500 × 500 grid The transmission range K of each node is equal to 10 Each node is generating a new message for a randomly selected destination with an inter-arrival time distribution uniform in [1, Tmax] Tmax is varied from 10000 (low traffic) to 2000 (high traffic) to create traffic loads

19. Scenario B : Effect of Connectivity The size of the network is 200×200 and Tmax is fixed to 4000 (medium traffic load). The number of nodes M and transmission range K, are varied to evaluate the performance of all protocols in networks with a large range of connectivity characteristics, ranging from very sparse, highly disconnected networks, to almost connected networks.

20. Scenario B : Effect of Connectivity

21. Scenario B: Effect of Connectivity

22. Conclusion Conclusion: Spray and Wait yields lower delay than existing flooding and utility-based schemes, and significantly reduces transmissions delays close to the optimal can be achieved with few copies theory and simulations prove that it is scalable It is simple: can be optimized with little knowledge about the network Deficiency: The theoretic analysis and simulation only based on random movement model

23. Thank you